A Penalty-Free Pipeline for Direct Quantum-Annealer Portfolio Optimization

Abstract

Cardinality-constrained portfolio selection is routinely cast as a quadratic unconstrained binary optimization (QUBO) and submitted to a quantum processing unit (QPU) for direct annealing. We show that this standard penalty encoding is the binding constraint for direct-QPU execution on current D-Wave Pegasus and Zephyr hardware. Expanding the exact cardinality penalty contributes a dense rank-one term that makes the logical interaction graph complete regardless of the covariance, producing chain-break fractions from 83% at small universes up to 92% at the full forty-nine-industry Fama--French universe, and zero feasible raw samples at every tested scale. Topology-aware sparsification reduces chain breaks to near zero, but any sparsifier that removes off-diagonal entries also dilutes the cardinality constraint; an ablation reveals that this sparsify-and-project pipeline is dominated by the classical projector, not the QPU. We propose removing the penalty entirely: sample an objective-only QUBO built from expected returns and the risk-scaled covariance on hardware, and enforce cardinality classically through a deterministic feasibility projector. Across 4,468 saved embedding records on live Pegasus and Zephyr hardware, spanning equities up to forty-nine assets and football-betting instances up to forty-eight, this penalty-free pipeline reduces mean chain-break fractions from 71%--92% down to at most 0.04%, and post-processed regret is at most 0.03% relative to greedy classical references at every tested scale. We do not claim quantum advantage; the penalty encoding, not the sparse hardware topology, is the limiting factor for direct-QPU portfolio optimization at currently accessible scales.